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Earth's Curvature Formula:
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The Earth's curvature refers to the gradual drop in height due to the spherical shape of the Earth as you look across distances. This calculator estimates how much the Earth's surface drops below a flat horizontal plane over a given distance.
The calculator uses the simple curvature formula:
Where:
Explanation: This formula approximates the vertical drop from a tangent line at the starting point. For more precise calculations over long distances, more complex formulas accounting for refraction and observer height are needed.
Details: Understanding Earth's curvature is important for surveying, astronomy, photography, and verifying visibility of distant objects. It's also relevant for understanding why distant objects disappear bottom-first over the horizon.
Tips: Enter distance in meters (1 km = 1000 m) and Earth's radius (default is standard value). For most purposes, the default Earth radius is sufficient.
Q1: How accurate is this simple formula?
A: It's quite accurate for distances up to about 100 km. For longer distances, more complex formulas accounting for refraction and observer height are needed.
Q2: Why does the drop increase with the square of distance?
A: This is a geometric property of circles - the vertical drop increases more rapidly than the linear distance along the surface.
Q3: Does this account for atmospheric refraction?
A: No, this simple formula doesn't account for refraction, which can make distant objects appear slightly higher than they actually are.
Q4: How much does the Earth curve per kilometer?
A: For 1 km (1000 m), the drop is about 7.8 cm. For 10 km, it's about 7.8 meters (100 times more, since drop increases with distance squared).
Q5: Can I see this curvature from high altitudes?
A: The curvature becomes visible to the naked eye at altitudes above about 10-15 km (35,000-50,000 feet).